1. Throughput Profit Multiplier Based on the books: Building Lean Supply Chains with the Theory of Constraints Managing Business Process Flow

2. Throughput Profit Multiplier (TPM)
A large fraction of the operating costs are fixed  small changes in throughput could be translated into large changes in profits.
Throughput profit multiplier (TPM) =
TPM = % Changes in Profit/ % Changes in Throughput
% Changes in Profit = (Profit2-Profit1)/Profit1
% Changes in Throughput = (Throughput2-Throoughput1)/Throughput1
TPM = (Prof2-Prof1)/Prof1]/[ (Q2-Q1)/Q1]
Suppose fixed cost F = $180,000 per month. Sales price per unit P = 22, and variable cost per unit V = 2. In July, the process throughput was 10,000 units. A process improvement increased throughput in August by 2% to 10,200 units without any increase in the fixed cost. Compute throughput profit multiplier.

3. Financial Throughput and Fixed Operating Costs
We define financial throughput as the rate at which the enterprise generates money. By selling one unit of product we generate P dollars, at the same time we incur V dollars pure variable cost. Pure variable cost is the cost directly related to the production of one additional unit - such as raw material. It does not include sunk costs such as salary, rent, and depreciation. Since we produce and sell Q units per unit of time. The financial throughput is Q(P-V).
Fixed Operating Expenses (F) include all costs not directly related to production of one additional unit. That includes costs such as human and capital resources.
In our example, F = $180,000 per month, P = 22, and V = 2. In July, financial throughput was 10,000(22-2) = 200,000. In August R increased by 2%.

4. Another Look at Throughput Profit Multiplier
Financial throughput is (22-2)10000 =
Fixed Operating Expense =
In this example, Fixed Operating Expense is 90% of Financial Throughput.
F= 0.9(P-V)Q
Profit = 10% of financial throughput. Profit = 0.1(P-V)Q
If Q increases by 1% Financial throughput increases by 1% too, and it is all profit because we have already covered all fixed operating expenses.
Therefore increase in profit = 0.01(P-V)Q, and % change in profit = 0.01(P-V)Q/0.1(P-V)Q =0.1 = 10%.
1% change in Throughput, 10% change in profit.
2% increase in throughput  20% increase in profit.

5. Throughput Profit Multiplier
Let us summarize our notations (these notations benefit from E. Goldratt and M. M. Srinivasan)
Throughput: Q
Fixed Operating Expenses; cost of human resources and depreciation of capital resources plus all other indirect costs: F
Total Revenue: PQ
Total Cost: VQ+F
Profit Margin; the money generated by producing (and selling) additional unit : P-V
Financial throughput. The rate at which the enterprise generates money: (P-V)Q
Profit = (P-V)Q-F

6. Relationship Between Financial Throughput and Fixed Operation Expenses
Suppose F/Financial-Throughput = y = F/(P-V)Q = y; 1>y >0
Therefore, F = y(P-V)Q
Profit = (P-V)Q-F = (P-V)Q - y(P-V)Q = (1-y)(P-V)Q
If % increase in throughput is x%.
Then the increase in profit is x(P-V)Q.
% change in profit = [x(P-V)Q]/[(1-y)(P-V)Q]
% change in profit = x/(1-y)
TPM = % change in profit /% changes in throughput
TPM = [x/(1-y)]/x
TPM = 1/(1-y)

7. Problem 5.6
A company's average costs and revenues for a typical month are $15 million and $18 respectively. It is estimated that 1/3 of the costs are variable and the rest are fixed. What is the throughput profit multiplier?
Total Variable Cost =VQ = 5,000,000
Fixed Operating Expenses =F = $10,000,000
Total Revenue = PQ = $18,000,000
Financial Throughput = (P-V)Q = PQ-VQ = $18,000,000-5,000,000 = 13,000,000
F/(P-V)Q = $10,000,000/ 13,000,000 = 10/13
TPM = 1/(1-y) = 1/(1-10/13) = 13/3
If throughput increases by 1% profit will increase by 4.33%.

8. A Viable Vision
A Viable Vision (Goldratt): What if we decide to have todays total revenue as tomorrows total profit.
In our example, Financial Throughput in July was Q1(P-V) = 10,000(22-2). In order to have your profit equal this amount we need to produce Q2 units such that:
Q2(P-V) – F = Q1(P-V)
Q2(20) -180,000 = 10,000(20)
Q2(20) = 380,000
Q2 = 19,000
In order to have your todays total revenue as tomorrows total profit. We should increase our sales by (19,000-10,000)/10,000 = 90%. If we almost double our sales, our current revenue becomes our tomorrows profit.

9. A Viable Vision- Goldratt
Decide to have your todays total revenue as your tomorrows total profit. What should your sales be equal to?
Todays Throughput =R, Today’s Revenue = PR
Target Profit = (P-V}R2-F, Target Throughput =R2 = (1+x)R
F= y(P-V)R  PR2-F = (P-V) (1+x) R-y(P-V)R
(P –V)(1+x)R-y(P-V)R= (P –V)R[1+x-y)=PR
1+x-y = P/(P-V)  x = P/(P-V)-1 +y
x = V/(P-V) +y
If V= zP then, x = zP/(P-zP) +y = z/(1-z)+y
In our example, P=22, V=2  z =1/11, z/(1-z) = 0.1, F = 180,000, R =10,000, F = 0.9(P-V)  y=0.9  x = = 1.
If R is doubled, todays revenue becomes tomorrows profit.

10. A Viable Vision
If Variable cost is less than 60% of the sales prose, the viable vision is achievable by incensing the throughput by less than 2.5x.